Measurement of quantum correlation by Frobenius norm in non-Markovian system

2018 ◽  
Vol 16 (03) ◽  
pp. 1850022 ◽  
Author(s):  
Juju Hu ◽  
Shuqin Liu ◽  
Yinghua Ji
Keyword(s):  
Density Matrix ◽  
Quantum System ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Frobenius Norm ◽  
Easy Method ◽  
Test Matrix ◽  
Research Results ◽  
Bipartite State ◽  
Markovian System

In order to measure the quantum correlation of a bipartite state quickly, an easy method is to construct a test matrix through the commutations among the blocks of its density matrix. Then, the Frobenius norm of the test matrix can be used to measure the quantum correlation. In this paper, we apply the measurement by Frobenius norm ([Formula: see text] to the dynamics evolution of the non-Markovian quantum system and compare it with the typical quantum discord ([Formula: see text] proposed by Ollivier and Zurek. The research results show that [Formula: see text] can indeed measure the quantum correlation of a bipartite state as same as [Formula: see text]. Further studies find that there are still differences between the two measurements: in some regions, when [Formula: see text] is zero, [Formula: see text] is not zero. It indicates that [Formula: see text] is more detailed than [Formula: see text] to measure quantum correlation of a bipartite state.

scholarly journals SUDDEN CHANGE OF QUANTUM DISCORD UNDER SINGLE QUBIT NOISE

2013 ◽  
Vol 11 (05) ◽  
pp. 1350048 ◽  
Author(s):  
LI-XING JIA ◽  
BO LI ◽  
R.-H. YUE ◽  
HENG FAN
Keyword(s):  
Quantum System ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Sudden Change ◽  
Entangled State ◽  
Noisy Environment ◽  
Noisy Environments ◽  
Single Qubit ◽  
Sudden Transition

We show that the sudden change of quantum correlation can occur even when only one part of the composite entangled state is exposed to a noisy environment. Our results are illustrated through the action of different noisy environments individually on a single qubit of quantum system. Composite noise on the whole of the quantum system is thus not the necessarily condition for the occurrence of sudden transition for quantum correlation.

Sudden change in the behavior of quantum discord for bipartite Gisin states

2018 ◽  
Vol 15 (03) ◽  
pp. 1850038 ◽  
Author(s):  
Fatima-Zahra Siyouri ◽  
Mustapha Ziane ◽  
Morad El Baz ◽  
Yassine Hassouni
Keyword(s):  
Quantum System ◽  
Quantum Correlation ◽  
Coherent States ◽  
Quantum Discord ◽  
Sudden Change ◽  
Classical Correlation ◽  
Mixing Parameter

In this paper, we investigate the behavior of quantum correlation for Gisin states based on the bipartite superposed coherent states (SCS). Moreover, we analyze the basis for minimizing the quantum discord (or equivalently basis maximizing the classical correlation) as function of the mixing parameter and the coherent amplitude. We found that for our quantum system, the quantum discord behavior is not smooth and could experience a sudden change (S.C).

The impact of resource on remote quantum correlation Preparation

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1223-1232
Author(s):  
Chengjun Wu ◽  
Bin Luo ◽  
Hong Guo
Keyword(s):  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Entangled States ◽  
Shared Resources ◽  
Classical Communication ◽  
Bell Measurement ◽  
Measurement Results ◽  
The Impact

When Alice and Bob share two pairs of quantum correlated states, Alice can remotely prepare quantum entanglement and quantum discord in Bob’s side by measuring the parts in her side and telling Bob the measurement results by classical communication. For remote entanglement preparation, entanglement is necessary . We find that for some shared resources having the same amount of entanglement, when Bell measurement is used, the entanglement remotely prepared can be different, and more discord in the resources actually decreases the entanglement prepared. We also find that for some resources with more entanglement, the entanglement remotely prepared may be less. Therefore, we conclude that entanglement is a necessary resource but may not be the only resource responsible for the entanglement remotely prepared, and discord does not likely to assist this process. Also, for the preparation of discord, we find that some states with no entanglement could outperform entangled states.

Improvement of quantum correlations by repetitive quantum error correction

2019 ◽  
Vol 17 (05) ◽  
pp. 1950044
Author(s):  
A. El Allati ◽  
H. Amellal ◽  
A. Meslouhi
Keyword(s):  
Error Correction ◽  
Quantum Correlation ◽  
Coherent States ◽  
Quantum Discord ◽  
Error Correcting Code ◽  
Quantum Correlations ◽  
Quantum Error Correction ◽  
Optical Field ◽  
Quantum Error ◽  
Entangled Coherent States

A quantum error-correcting code is established in entangled coherent states (CSs) with Markovian and non-Markovian environments. However, the dynamic behavior of these optical states is discussed in terms of quantum correlation measurements, entanglement and discord. By using the correcting codes, these correlations can be as robust as possible against environmental effects. As the number of redundant CSs increases due to the repetitive error correction, the probabilities of success also increase significantly. Based on different optical field parameters, the discord can withstand more than an entanglement. Furthermore, the behavior of quantum discord under decoherence may exhibit sudden death and sudden birth phenomena as functions of dimensionless parameters.

scholarly journals The freezing Rènyi quantum discord

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Xiao-Yu Li ◽  
Qin-Sheng Zhu ◽  
Ming-Zheng Zhu ◽  
Hao Wu ◽  
Shao-Yi Wu ◽  
...  
Keyword(s):  
Quantum Correlation ◽  
Quantum Discord ◽  
Universal Quantum

Abstract As a universal quantum character of quantum correlation, the freezing phenomenon is researched by geometry and quantum discord methods, respectively. In this paper, the properties of Rènyi discord is studied for two independent Dimer System coupled to two correlated Fermi-spin environments under the non-Markovian condition. We further demonstrate that the freezing behaviors still exist for Rènyi discord and study the effects of different parameters on this behaviors.

REVIEW ON SYSTEM-SPIN ENVIRONMENT DYNAMICS OF QUANTUM DISCORD

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345055 ◽  
Author(s):  
BEN-QIONG LIU ◽  
BIN SHAO ◽  
JUN-GANG LI ◽  
JIAN ZOU
Keyword(s):  
Quantum Discord ◽  
Open Systems ◽  
Quantum Phase Transitions ◽  
Physical Models ◽  
Quantum Computers ◽  
Bipartite State ◽  
External Perturbations ◽  
Mathematical Properties ◽  
Spin Pairs ◽  
The Relationship

Recent work has relatively comprehensively studied the quantum discord, which is supposed to account for all the nonclassical correlations present in a bipartite state (including entanglement), and provide computational speedup and quantum enhancement even in separable states. Firstly, we introduce several different indicators of nonclassical correlations, including their definitions and interpretations, mathematical properties, and the relationship between them. Secondly, we review two major topics of quantum discord. One is the remarkable behavior at quantum phase transitions. The pairwise quantum discord for nearest neighbors as well as distant spin pairs can perfectly signal the critical behavior of many physical models, even at finite temperatures. The other is quantum discord dynamics in open systems, especially for "system-spin environment" models. Quantum discord is more robust than entanglement against external perturbations. It can be created, greatly amplified or protected under certain conditions, and presents promising applications in quantum technologies such as quantum computers.

QUANTUM CORRELATIONS IN THE ENTANGLEMENT DISTILLATION PROTOCOLS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350029
Author(s):  
SHAO-XIONG WU ◽  
JUN ZHANG ◽  
CHANG-SHUI YU ◽  
HE-SHAN SONG
Keyword(s):  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Entangled States ◽  
Entanglement Distillation

We study the quantum correlations between source and target pairs in different protocols of entanglement distillation of one kind of entangled states. We find that there does not exist any quantum correlation in the standard recurrence distillation protocol, while quantum discord and even quantum entanglement are always present in the other two cases of the improved distillation protocols. In the three cases, the distillation efficiency improved with the quantum correlations enhanced.

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